Pricing, bundling, and driver behavior in crowdsourced delivery

TL;DR

This paper develops an integrated optimization model for crowdsourced last-mile delivery, focusing on task bundling, driver acceptance, and compensation to maximize cost savings, and introduces tailored algorithms to solve complex instances efficiently.

Contribution

It formulates a novel mixed-integer nonlinear program for joint bundling and compensation decisions, and proposes an exact linearization with a specialized column generation algorithm.

Findings

Algorithms solve instances with up to 120 tasks and 60 drivers efficiently.

Integrated decision-making outperforms sequential approaches.

Compensation significantly influences bundle structure.

Abstract

Challenges in last-mile delivery have encouraged innovative solutions like crowdsourced delivery, where online platforms leverage the services of drivers who occasionally perform delivery tasks for compensation. A key challenge is that occasional drivers' acceptance behavior towards offered tasks is uncertain and influenced by task properties and compensation. The current literature lacks formulations that fully address this challenge. Hence, we formulate an integrated problem that maximizes total expected cost savings by offering task bundles to occasional drivers. To this end, we simultaneously determine the optimal bundle set, their assignment to occasional drivers, and compensations for each pair while considering acceptance probabilities, which are captured via generic logistic functions. The vast number of potential bundles, combined with incorporating acceptance probabilities leads to a mixed-integer nonlinear program (MINLP) with exponentially many variables. Using mild assumptions, we address these complexities by exploiting properties of the problem, leading to an exact linearization of the MINLP which we solve via a tailored exact column generation algorithm. Our algorithm uses a variant of the elementary shortest path problem with resource constraints (ESPPRC) that features a non-linear and non-additive objective function as its subproblem, for which we develop tailored dominance and pruning strategies. We introduce several heuristic and exact variants and perform an extensive set of experiments evaluating the algorithm performances and solution structures. The results demonstrate the efficiency of the algorithms for instances with up to 120 tasks and 60 drivers and highlight the advantages of integrated decision-making over sequential approaches. The sensitivity analysis indicates that compensation is the most influential factor in shaping the bundle structure.